Problem Solving

No need to pick numbers here. Can be done directly.

Cost to produce a batch of 20,000 tools = $10,000 + $3(20,000) = $70,000
Selling price for 20,000 tools = $8(20,000) = $160,000
Gross profit earned = $160,000 - $70,000 = $90,000
Therefore, gross profit per tool = $90,000/ 20,000 = $4.50

The correct answer is [spoiler](C)[/spoiler].

pullagurla wrote:The total cost for Company X to produce a batch of
tools is $10,000 plus $3 per tool. Each tool sells for
$8. The gross pro� t earned from producing and selling
these tools is the total income from sales minus the
total production cost. If a batch of 20,000 tools is
produced and sold, then Company X's gross pro� t per
tool is
(A) $3.00
(B) $3.75
(C) $4.50
(D) $5.00
(E) $5.50

We can use the following formula:

Profit = (number of tools sold)(revenue per tool) - [fixed cost + (number of tools made)(cost per tool)]

We are given the following:

fixed cost = $10,000

cost per tool = $3

revenue per tool = $8

Number of tools produced and sold = 20,000

We can now plug all this into our profit equation:

Profit = (number of tools sold)(revenue per tool) - [fixed cost + (number of tools made)(cost per tool)]

P = 20,000 x 8 - [10,000 + (3 x 20,000)]

P = 20,000 x 8 - [10,000 + (3 x 20,000)]

P = 160,000 - [10,000 + 60,000]

P = 160,000 - 70,000

P = 90,000

Since the total profit is $90,000 and 20,000 tools are produced and sold, the profit per tool is 90,000/20,000 = 9/2 = $4.50

Alternate Solution:

If there were no fixed costs, the profit per tool would be the selling price minus the cost to make each tool, or $8 - $3 = $5. However, the total fixed cost of $10,000 must be "absorbed" by the tools that are sold. Since 20,000 tools were sold, the fixed cost that each tool must "absorb" is $10,000/20,000, or $0.50 per tool. Thus, the profit per tool is $8 - $3 - $0.50 = $4.50.

Answer: C

Hi All,

We're told that the total cost for Company X to produce a batch of tools is $10,000 plus $3 per tool and that each tool sells for $8. The gross pro�t earned from producing and selling these tools is the total income from sales minus the total production cost and a batch of 20,000 tools is produced and sold. We're asked for Company X's gross pro�t per tool.

When a GMAT question gives you all of the 'numbers' needed to perform a calculation, there is often a 'shortcut' that you can use to save time on the 'math' - but you have to really consider the information that you're given. Here, we know that each tool costs $3 to make and brings in $8 in revenue. Thus, each tool nets us $5.

With 20,000 tools, that would be a profit of ($5)(20,000) = $100,000
When we subtract out the initial fixed costs of $10,000, we have a TOTAL PROFIT of $100,000 - $10,000 = $90,000
On a per-tool basis, that profit is $90,000/20,000 = $9/2 = $4.50 per tool

Final Answer: C

GMAT assassins aren't born, they're made,
Rich